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Predecessor & Successor

The successor...

Question

The successor of 1001 is
(a) 1000
(b) 1002
(c) none of these

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Solution

(b) 1002

Successor of 1001 = 1001 + 1 = 1002

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Q. The coefficient of

x^{50}

in the expansion of

(1 + x)^{1000} + 2 x (1 + x)^{999} + 3 x^{2} (1 + x)^{998} + . . . . . . + 1001 x^{1000}

Q. Coefficient of

x^{2009}

(1 + x + x^{2} + x^{3} + x^{4})^{1001} (1 - x)^{1002}

Q. The LCM of 100 and 101 is
(a) 10100
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(a) 7
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(c) 847
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